About halfway through the interview (30:20), Scherz explains his view of "the scientific method:"
"You take the data, you take all the data, you analyze the data, and you come up and see where that analysis goes: that is what is truth."
Pulitzer follows up by bemoaning the fate of "our young people" who are not being taught science. Throughout the interview the pair discuss how "science" will eventually render archaeology and anthropology obsolete.
It's very dramatic.
It's also very wrong. Neither of these guys seems to actually understand what science is. There are a lot of different definitions and conceptions of science, but most of them share some core components. Science is a systematic way of acquiring knowledge about the natural world. It has to have embedded somewhere in it a mechanism for falsification (proving things wrong). Falsification allows science to be cumulative: it builds on itself because we can discard ideas that have been shown to be false.
In the quote above, Scherz is not describing "the scientific method," he's describing induction. Induction is an important part of science. When you're working on the inductive side, you have a pile of information in front of you and you sort through it and try to construct a story that makes sense and accommodates all that information.
Inducing things (constructing general explanations that accommodate data) is great, but it's only half the battle when you're actually trying to do science. After you construct that general explanation, you need to figure out a way to test it. You need to deduce what the implications of the general explanation are and then try to test those implications. You need to say something like "if my explanation X is correct, I would expect a, b, and c to be true." Then you actually need to go and check if a, b, and c are true. If they aren't, there's something wrong with your general explanation (i.e., it isn't complete or correct) or your underlying assumptions.
When archaeology is done as a science, it includes a back-and-forth between induction and deduction. It doesn't really matter where an idea comes from as long as you can test it.
When Scherz says that science is basically the distillation of "truth" from looking at a bunch of data, he is betraying the presence of a fundamental misunderstanding that I think is shared by many "fringe" theorists. If you're one of those people, ask yourself this question: what piece of evidence would prove your idea wrong? If you can't think of one, you've got a problem.
A single good site in the Americas would falsify the idea that people from Civilization X or Civilization Y made it to New World before Columbus. Discovery and excavation of the site of L'Anse aux Meadows, for example, pretty much sealed the deal for the idea that the Norse made it to North America. When you phrase the hypothesis as "The Norse never made it to North America," you can falsify it by finding a site that proves they did. In other words, evidence can be used to falsify the hypothesis.
The reverse is not true. The hypothesis "The Minoans made it to North America" cannot be falsified because neither I nor anyone else can produce a piece of evidence that proves that the Minoans weren't here. All I can do is ask "what is your evidence that it did happen?" If that evidence is some re-labeled photos, or some tablets that have been shown to be fraudulent, you really haven't met even the minimum threshold for having a serious discussion about the merits of your idea. If the strongest "evidence" that you can produce is a laundry list of problematic artifacts (some of which are known frauds), can you really be that surprised that very few people outside of the "safe zone" of the AAPS conference take your work seriously?
If there's no mechanism for evaluating an inductively-constructed explanation, the quality of the evidence of the source of the idea matter. In the last half of the interview, Scherz rattles off a list of "evidence" that includes the Kensington Rune Stone, the "Detroit plates" (he may be referring to the Michigan Relics aka the Soper Frauds), the Newark Holy Stone, and the artifacts from Burrows Cave. It's the same list we've heard for years.
I presume that not all "fringe" theorists accept as genuine all of the artifacts and sites that are put forward as evidence of pre-Columbian transoceanic contact. If that's correct, then by what mechanisms do you determine what is genuine and what is not? Is there any interest in critical examination of pieces of evidence? Are there any artifacts out there that all "fringe" theorists agree are fake? Do you take into account the possibility that fake artifacts exist? If so, what do you do about it?
Sadly, I've seen very little evidence that there exists much of an appetite among "fringe" theorists to critically evaluate their evidence (or even bother to read the critical evaluations of others). Pulitzer has already demonstrated that he has no interest in weeding out fakery, and has now become a support of Burrows Cave (apparently based on the argument that a modern forger would have been unable to trace a map of the Great Lakes). I fear that if there was a good piece of evidence for something interesting floating around out there it would get lost among all shouting about the nonsense.
It seems to me that the path to "truth" is going to pretty hard to follow if it's paved with artifacts that are made up. Good luck with that.